Three identical lightbulbs, labeled A, B, and C, are connected to an ideal 12 V battery as follows: bulb A is placed in series with a branch that contains bulbs B and C in parallel. Assume each bulb has resistance R that remains essentially constant over the operating range and the connecting wires have negligible resistance.
(1) Determine the equivalent resistance of the parallel combination consisting of bulbs B and C, expressing your answer in terms of R. Briefly explain your reasoning.
(2) Without doing any explicit numerical calculations, rank the magnitudes of the current through bulbs A, B, and C from greatest to least. Justify your ranking with qualitative arguments based on the circuit arrangement identified in part (a).
(3) Using appropriate physical reasoning, rank the power dissipated by each bulb from greatest to least. Clearly describe the principles you use to arrive at your ranking.
(4) Explain how the power delivered by the battery compares with the total power dissipated by the three bulbs. Your answer should make explicit reference to the conservation of energy in electric circuits.